The conditional value-at-risk (CVaR) at a quantile level \(q \in (0,1]\)  is a mapping from \(\mathcal {L}^1(\Omega , \mathcal {F}, \mathbb {P})\)  to \(\mathbb {R}\) .
While there exist several definitions of CVaR in the literature, we consider the one based on its dual representation as a coherent risk measure [1]}, [2]}: given a random variable \(C \in \mathcal {L}^1\) ,
\( \operatorname{\mathrm {CVaR}}_q[C] \triangleq \sup _{Q^\dagger \in \mathcal {Q}^\dagger (q)} \mathbb {E}\left[ C Q^\dagger \right]\quad \text{where} \quad \mathcal {Q}^\dagger (q) \triangleq \left\lbrace  Q^\dagger \in \mathcal {L}^\infty (\Omega , \mathcal {F}, \mathbb {P}), ~ 0 \le Q^\dagger \le \frac{1}{q}, ~ \mathbb {E}Q^\dagger = 1 \right\rbrace ,\) 
